If a pair of perpendicular straight lines drawn through the origin forms an isosceles triangle with the line `2x+3y=6` , then area of the triangle so formed is 36/13 (b) 12/17 (c) 13/5 (d) 17/14

Options

A. `(36)/(13) " sq. unit"`
B. `(12)/(17) " sq. unit"`
C. `(13)/(5) " sq. unit"`
D. `(17)/(13) " sq. unit"`

Answer

A

Explanation

As shown in the following figure, pair of perpendicular lines through origin meets given line 2x+3y=6 at A and B such that AOB is right angled isosceles triangle.

Now, OM=BM=AM, where OM `=(|0+0-6|)/(sqrt(2^(2) + 3^(2))) = (6)/(sqrt(13))`
`therefore AB=2AM=2OM = (12)/(sqrt(13))`
`therefore " Area of triangle "AOB = (1)/(2) xx (12)/(sqrt(13)) xx (6)/(sqrt(13)) = (36)/(13)` sq. units.